• Journal of the Korean Mathematical Society
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• v.39 no.1
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• pp.91-102
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• 2002

Let M and N be CR manifolds with nondegenerate Levi forms of hypersurface type of dimension 2m ＋ 1 and 2n ＋ 1, respectively, where 1 $\leq$ m $\leq$ n. Let f : M longrightarrow N be a CR mapping. Under a generic assumption we construct a complete system of finite order for the infinitesimal deformations of f. In particular, we prove the space of infinitesimal deformations of f forms a finite dimensional Lie algebra.

• Journal of the Chungcheong Mathematical Society
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• v.28 no.2
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• pp.307-310
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• 2015

Let H be a color Poisson bialgebra. Here we find a canonical nondegenerate bilinear form $\mathfrak{g}(H){\times}\mathfrak{m/m^2}$, where $\mathfrak{g}(H)$ and $\mathfrak{m/m^2}$ are certain color Lie algebras induced by H.

• Journal of the Korean Mathematical Society
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• v.43 no.6
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• pp.1301-1324
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• 2006

The affine homogeneous hypersurface in ${\mathbb{R}}^{n+1}$, which is a graph of a function $F:{\mathbb{R}}^n{\rightarrow}{\mathbb{R}}$ with |det DdF|=1, corresponds to a complete unimodular left symmetric algebra with a nondegenerate Hessian type inner product. We will investigate the condition for the domain over the homogeneous hypersurface to be homogeneous through an extension of the complete unimodular left symmetric algebra, which is called the graph extension.

• Journal of applied mathematics & informatics
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• v.33 no.1_2
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• pp.229-234
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• 2015

In the setting of semidefinite linear complementarity problems on $S^n$, we focus on the Stein Transformation $S_A(X):=X-AXA^T$ for $A{\in}R^{n{\times}n}$ that is positive semidefinite preserving (i.e., $S_A(S^n_+){\subseteq}S^n_+$) and show that such transformation is strictly monotone if and only if it is nondegenerate. We also show that a positive semidefinite preserving $S_A$ has the Ultra-GUS property if and only if $1{\not\in}{\sigma}(A){\sigma}(A)$.

• Journal of the Optical Society of Korea
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• v.1 no.1
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• pp.1-4
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• 1997

The theoretical limit of the noise correlation between the signal and idler outputs of a nondegenerate optical parametric amplifier (NOPA) with a coherent state signal and vacuum state idler input can be enhanced if a non-vacuum coherent state idler input is employed. By choosing a balanced signal and idler input, the noise correlation is $1/{({\root}g + {\root}{g-1})}^2$, where g is the intensity gain of the NOPA, and that is superior to the prediced outputs with single signal input by approximately 3dB. The result is applicable to all the schemes that use the NOPA to produce a sub-shot noise light generation such as feed-back or feed-forward control.

• Korean Journal of Optics and Photonics
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• v.10 no.4
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• pp.294-300
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• 1999

The density matrix is solved more rigorously, compared with the third-order pertubation method used in the conventional theory, for a semiconductor laser amplifier. Then the coupled wave equations are derived to explain the wavelength conversion due to the spectral hole burning in the semiconductor optical amplifier. It is shown that our results can explain the effect of saturation of the population density on the electric polarization, which affects the four-wave mixing and wavelength conversion, better than the conventional theroy where the third-order pertubation is used.

• Proceedings of the Korean Magnestics Society Conference
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• 2010.06a
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• pp.96-96
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• 2010

We report the proper resistance-area products in the single crystalline bcc CoFe/MgO tunnel contact on nondegenerate n-Ge desirable for efficient spin injection and detection at room temperature. The electric properties of the crystalline CoFe(5 nm)/MgO(1.5,2.0,2.5 nm)/n-Ge(001) tunnel contacts have been investigated by I-V-T and C-V measurements. Interestingly, the tunnel contact with the 2-nm MgO exhibits the ohmic behavior with low resistance-area products, satisfying the theoretical conditions required for significant spin injection and detection. This result is ascribed to the presence of MgO layer between CoFe and n-Ge, enhancing the Schottky pinning parameter as well as shifting the charge neutrality level.

• Communications of the Korean Mathematical Society
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• v.11 no.4
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• pp.1061-1066
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• 1996

We will give an example which is a normal Hausdorff countable dense homogeneous space but not a densely homogeneous space. Next, we will give a proof for the fact that every nondegenerate component of densely homogenous spaces is open and densely homogeneous.

• Journal of the Korean Mathematical Society
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• v.37 no.2
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• pp.225-243
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• 2000

We explain the notion of complete system and how it naturally arises from the equivalence problem of G-structures. Then we construct a complete system of 3rd order for the infinitesimal CR automorphisms of CR manifold of nondegenerate Levi form.

• Proceedings of the Optical Society of Korea Conference
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• 2001.08a
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• pp.240-241
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• 2001